Question

A 300-foot cable weighing 6 pounds per foot is hanging from a winch 300 feet above ground level. Find the work (in ft-lb) done in winding up the cable when there is a 200-pound load attached to the end of the cable.

Answer 1

Step-by-step explanation:

Given

Length of cable
`L=300 ft`

Weight density
`\lambda =6 pound/ft`

Winch height
`h=300 ft`

additional load
`W=200\ pound`

Work done

`W=\int_(0)^(300)\lambda ydy+W* distance\ moved`

`W=\int_(0)^(300)6\cdot ydy+200* 300`

`W=3\left [ y^2\right ]^(300)_(0)+60,000`

`W=3,30,000 lb-ft`